Suppose the roots of the polynomial \(x^2 - mx + n\) are positive prime integers (not necessarily distinct). Given that \(m < 20\) , how many possible values of \(m\) are there? (woops sorry I forgot the m)
I THINK you meant how many possible values of 'n' are there?
Since the two roots are positive....
this means the solution looks like this:
(x-a)(x-b) where a and b are the roots
a and b must ADD to m and must multiply to n AND m<20 or <=19 and POSITIVE integers AND PRIME
primes below 19
3 5 7 11 13 17 19 Two of these added together must be <= to 19
3 + 3,7,11,13
5 + 5,7,11,13
I think that is all the combos ====> TEN possible values of 'n' (only 6 values of 'm')